Reminder Round all answers to two decimal places unless otherwise indicated.
Eagles In an effort to restore the population of bald eagles, ecologists introduce a breeding group into a protected area. Let
♣ Initially,
♣ A few years later,
♣ Many years later,
Make a possible graph of
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.arrow_forwardpH of Saliva The pH of saliva is normally in the range of 6.4 to 7.0. However, when a person is ill, the persons saliva becomes more acidic. a When Marco is sick, he tests the pH of his saliva and finds that it is 5.5. What is the hydrogen ion concentration of his saliva? b Will the hydrogen ion concentration in Marcos saliva increase or decrease as he gets better? c After Marco recovers, he tests the pH of his saliva, and it is 6.5. Was the saliva more acidic or less acidic when he was sick?arrow_forwardOTHER APPLICATIONS Length of a Pendulum. A simple pendulum swings back and forth in regular time intervals. Grandfather clocks use pendulums to keep accurate time. The relationship between the length of a pendulum L and the period time T for one complete oscillation can be expressed by the function L=kTn where k is a constant and n is a positive integer to be determined. The data below were taken for different lengths of pendulums. Source: Gary Rockswold. Tsec L(ft) 1.11 1.0 1.36 1.5 1.57 2.0 1.76 2.5 1.92 3.0 2.08 3.5 2.22 4.0 a. Find the value of k for n=1,2,and3, using the data for the 4-ft pendulum.. b. Use a graphing calculator to plot the data in the table and to graph the function L=kTn for the three values of k and corresponding values of n found in part a. Which function best fits the data. c. Use the best fitting function from part a to predict the period of a pendulum having a length of 5ft. d. If the length of the pendulum doubles, what happens to the period? e. If you have a graphing calculator or computer program with a quadratic regression feature, use it to find a quadratic function that approximately fits the data. How does this answer compare with the answer to part b.arrow_forward
- Running Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner’s time at the each of each lap, obtaining the data in the following table. (a) What was the man’s average speed (rate) between 68 s and 152 s? (b) What was the man’s average speed between 263 s and 412 s? (c) Calculate the man’s speed for cadi lap, Is he slowing down, speeding up, or neither?arrow_forwardThermic Effect of Food The metabolic rate of a person who has just eaten a meal tends to go up and then, after some time has passed, return to a resting metabolic rate. This phenomenon is known as the thermic effect of food. Researchers have indicated that the thermic effect of food. Researchers have indicated that the thermic effect of food in kJ/hr for a particular person is F(t)=10.28+175.9tet/1.3 where t is the number of hours that have elapsed since eating a meal. Source: American Journal of Clinical Nutrition. a. Graph the function on [0,6] by [20,100]. b. Find the average rate of change of the thermic effect of food during the first hour after eating. c. Use a graphing calculator to find the instantaneous rate of change of the thermic effect of food exactly one hour after eating. d. Use a graphing calculator to estimate when the function stops increasing and begins to decrease.arrow_forward
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